LMFDB - Embedded newform 1728.2.z.a.719.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1728,2,Mod(143,1728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1728.143"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1728, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			719.10
Character	$\chi$	$=$	1728.719
Dual form			1728.2.z.a.1007.10

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.178044 - 0.664471i) q^{5} +(-0.645693 - 1.11837i) q^{7} +(0.860301 - 3.21069i) q^{11} +(1.27203 + 4.74727i) q^{13} +5.58523i q^{17} +(2.49649 + 2.49649i) q^{19} +(-2.36529 - 1.36560i) q^{23} +(3.92031 - 2.26339i) q^{25} +(0.792277 - 2.95682i) q^{29} +(5.28160 + 3.04933i) q^{31} +(-0.628165 + 0.628165i) q^{35} +(0.507420 + 0.507420i) q^{37} +(4.89892 - 8.48518i) q^{41} +(0.949956 + 0.254540i) q^{43} +(-6.13774 - 10.6309i) q^{47} +(2.66616 - 4.61793i) q^{49} +(-0.601793 + 0.601793i) q^{53} -2.28658 q^{55} +(4.77715 - 1.28003i) q^{59} +(10.8292 + 2.90167i) q^{61} +(2.92795 - 1.69045i) q^{65} +(-0.110351 + 0.0295686i) q^{67} +0.0447904i q^{71} -13.2931i q^{73} +(-4.14624 + 1.11098i) q^{77} +(2.50052 - 1.44368i) q^{79} +(3.79568 + 1.01705i) q^{83} +(3.71122 - 0.994419i) q^{85} +12.7362 q^{89} +(4.48788 - 4.48788i) q^{91} +(1.21436 - 2.10333i) q^{95} +(4.41066 + 7.63949i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.178044	−	0.664471i	−0.0796239	−	0.297161i	0.914618	−	0.404319i	$-0.132491\pi$
$5$	−0.178044	−	0.664471i	−0.0796239	−	0.297161i	−0.994242	+	0.107158i	$0.965825\pi$
$6$		0			0
$7$	−0.645693	−	1.11837i	−0.244049	−	0.422705i	0.717815	−	0.696234i	$-0.245142\pi$
$7$	−0.645693	−	1.11837i	−0.244049	−	0.422705i	−0.961864	+	0.273529i	$0.911809\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.860301	−	3.21069i	0.259390	−	0.968058i	−0.706205	−	0.708008i	$-0.749594\pi$
$11$	0.860301	−	3.21069i	0.259390	−	0.968058i	0.965595	−	0.260051i	$-0.0837392\pi$
$12$		0			0
$13$	1.27203	+	4.74727i	0.352797	+	1.31666i	0.883234	+	0.468933i	$0.155361\pi$
$13$	1.27203	+	4.74727i	0.352797	+	1.31666i	−0.530437	+	0.847725i	$0.677972\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			5.58523i			1.35462i	0.735699	+	0.677308i	$0.236854\pi$
$17$			5.58523i			1.35462i	−0.735699	+	0.677308i	$0.763146\pi$
$18$		0			0
$19$	2.49649	+	2.49649i	0.572733	+	0.572733i	0.932891	−	0.360158i	$-0.117277\pi$
$19$	2.49649	+	2.49649i	0.572733	+	0.572733i	−0.360158	+	0.932891i	$0.617277\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.36529	−	1.36560i	−0.493197	−	0.284747i	0.232703	−	0.972548i	$-0.425243\pi$
$23$	−2.36529	−	1.36560i	−0.493197	−	0.284747i	−0.725900	+	0.687801i	$0.758576\pi$
$24$		0			0
$25$	3.92031	−	2.26339i	0.784061	−	0.452678i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.792277	−	2.95682i	0.147122	−	0.549067i	−0.852530	−	0.522679i	$-0.824933\pi$
$29$	0.792277	−	2.95682i	0.147122	−	0.549067i	0.999652	−	0.0263884i	$-0.00840066\pi$
$30$		0			0
$31$	5.28160	+	3.04933i	0.948604	+	0.547677i	0.892647	−	0.450757i	$-0.148846\pi$
$31$	5.28160	+	3.04933i	0.948604	+	0.547677i	0.0559568	+	0.998433i	$0.482179\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.628165	+	0.628165i	−0.106179	+	0.106179i
$36$		0			0
$37$	0.507420	+	0.507420i	0.0834193	+	0.0834193i	0.747585	−	0.664166i	$-0.231213\pi$
$37$	0.507420	+	0.507420i	0.0834193	+	0.0834193i	−0.664166	+	0.747585i	$0.731213\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.89892	−	8.48518i	0.765083	−	1.32516i	−0.175120	−	0.984547i	$-0.556031\pi$
$41$	4.89892	−	8.48518i	0.765083	−	1.32516i	0.940203	−	0.340616i	$-0.110635\pi$
$42$		0			0
$43$	0.949956	+	0.254540i	0.144867	+	0.0388170i	0.330524	−	0.943798i	$-0.392775\pi$
$43$	0.949956	+	0.254540i	0.144867	+	0.0388170i	−0.185657	+	0.982615i	$0.559441\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.13774	−	10.6309i	−0.895281	−	1.55067i	−0.833456	−	0.552586i	$-0.813641\pi$
$47$	−6.13774	−	10.6309i	−0.895281	−	1.55067i	−0.0618250	−	0.998087i	$-0.519692\pi$
$48$		0			0
$49$	2.66616	−	4.61793i	0.380880	−	0.659704i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.601793	+	0.601793i	−0.0826626	+	0.0826626i	−0.747229	−	0.664567i	$-0.768616\pi$
$53$	−0.601793	+	0.601793i	−0.0826626	+	0.0826626i	0.664567	+	0.747229i	$0.268616\pi$
$54$		0			0
$55$	−2.28658			−0.308322
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.77715	−	1.28003i	0.621932	−	0.166646i	0.0659263	−	0.997824i	$-0.479000\pi$
$59$	4.77715	−	1.28003i	0.621932	−	0.166646i	0.556006	+	0.831178i	$0.312333\pi$
$60$		0			0
$61$	10.8292	+	2.90167i	1.38653	+	0.371520i	0.873490	−	0.486842i	$-0.161851\pi$
$61$	10.8292	+	2.90167i	1.38653	+	0.371520i	0.513043	+	0.858363i	$0.328518\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.92795	−	1.69045i	0.363167	−	0.209675i
$66$		0			0
$67$	−0.110351	+	0.0295686i	−0.0134816	+	0.00361238i	−0.265554	−	0.964096i	$-0.585555\pi$
$67$	−0.110351	+	0.0295686i	−0.0134816	+	0.00361238i	0.252072	+	0.967708i	$0.418888\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			0.0447904i			0.00531565i	0.999996	+	0.00265782i	$0.000846013\pi$
$71$			0.0447904i			0.00531565i	−0.999996	+	0.00265782i	$0.999154\pi$
$72$		0			0
$73$		−	13.2931i		−	1.55585i	−0.628360	−	0.777923i	$-0.716274\pi$
$73$		−	13.2931i		−	1.55585i	0.628360	−	0.777923i	$-0.283726\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.14624	+	1.11098i	−0.472507	+	0.126608i
$78$		0			0
$79$	2.50052	−	1.44368i	0.281331	−	0.162426i	−0.352695	−	0.935738i	$-0.614735\pi$
$79$	2.50052	−	1.44368i	0.281331	−	0.162426i	0.634026	+	0.773312i	$0.281401\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.79568	+	1.01705i	0.416630	+	0.111636i	0.461043	−	0.887378i	$-0.347475\pi$
$83$	3.79568	+	1.01705i	0.416630	+	0.111636i	−0.0444135	+	0.999013i	$0.514142\pi$
$84$		0			0
$85$	3.71122	−	0.994419i	0.402539	−	0.107860i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.7362			1.35003			0.675017	−	0.737802i	$-0.264136\pi$
$89$	12.7362			1.35003			0.675017	+	0.737802i	$0.264136\pi$
$90$		0			0
$91$	4.48788	−	4.48788i	0.470458	−	0.470458i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.21436	−	2.10333i	0.124590	−	0.215797i
$96$		0			0
$97$	4.41066	+	7.63949i	0.447835	+	0.775673i	0.998245	−	0.0592215i	$-0.0188618\pi$
$97$	4.41066	+	7.63949i	0.447835	+	0.775673i	−0.550410	+	0.834895i	$0.685529\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.02523	+	1.88240i	0.699037	+	0.187306i	0.590799	−	0.806819i	$-0.298813\pi$
$101$	7.02523	+	1.88240i	0.699037	+	0.187306i	0.108238	+	0.994125i	$0.465479\pi$
$102$		0			0
$103$	−9.50698	+	16.4666i	−0.936750	+	1.62250i	−0.165267	+	0.986249i	$0.552849\pi$
$103$	−9.50698	+	16.4666i	−0.936750	+	1.62250i	−0.771483	+	0.636250i	$0.780485\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.28797	+	8.28797i	0.801228	+	0.801228i	0.983287	−	0.182060i	$-0.0582764\pi$
$107$	8.28797	+	8.28797i	0.801228	+	0.801228i	−0.182060	+	0.983287i	$0.558276\pi$
$108$		0			0
$109$	−14.3799	+	14.3799i	−1.37735	+	1.37735i	−0.528273	+	0.849074i	$0.677160\pi$
$109$	−14.3799	+	14.3799i	−1.37735	+	1.37735i	−0.849074	+	0.528273i	$0.822840\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.18778	+	1.26312i	0.205809	+	0.118824i	0.599362	−	0.800478i	$-0.295421\pi$
$113$	2.18778	+	1.26312i	0.205809	+	0.118824i	−0.393553	+	0.919302i	$0.628754\pi$
$114$		0			0
$115$	−0.486275	+	1.81480i	−0.0453454	+	0.169231i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.24637	−	3.60634i	0.572604	−	0.330593i
$120$		0			0
$121$	−0.0421101	−	0.0243123i	−0.00382819	−	0.00221021i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.63408	−	4.63408i	−0.414485	−	0.414485i
$126$		0			0
$127$		−	17.5157i		−	1.55427i	−0.629333	−	0.777135i	$-0.716672\pi$
$127$		−	17.5157i		−	1.55427i	0.629333	−	0.777135i	$-0.283328\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.21241	+	11.9889i	0.280669	+	1.04747i	0.951946	+	0.306266i	$0.0990796\pi$
$131$	3.21241	+	11.9889i	0.280669	+	1.04747i	−0.671277	+	0.741207i	$0.734254\pi$
$132$		0			0
$133$	1.18004	−	4.40397i	0.102322	−	0.381872i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.00063	−	8.66134i	−0.427232	−	0.739988i	0.569394	−	0.822065i	$-0.307178\pi$
$137$	−5.00063	−	8.66134i	−0.427232	−	0.739988i	−0.996626	+	0.0820768i	$0.973845\pi$
$138$		0			0
$139$	0.368654	+	1.37583i	0.0312688	+	0.116697i	0.979796	−	0.199998i	$-0.0640936\pi$
$139$	0.368654	+	1.37583i	0.0312688	+	0.116697i	−0.948528	+	0.316695i	$0.897427\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	16.3363			1.36611
$144$		0			0
$145$	−2.10578			−0.174876
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.48172	−	5.52986i	−0.121387	−	0.453024i	0.878298	−	0.478114i	$-0.158679\pi$
$149$	−1.48172	−	5.52986i	−0.121387	−	0.453024i	−0.999685	+	0.0250901i	$0.992013\pi$
$150$		0			0
$151$	−8.10127	−	14.0318i	−0.659272	−	1.14189i	−0.980804	−	0.194994i	$-0.937531\pi$
$151$	−8.10127	−	14.0318i	−0.659272	−	1.14189i	0.321533	−	0.946899i	$-0.395802\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.08583	−	4.05239i	0.0872163	−	0.325496i
$156$		0			0
$157$	−2.02762	−	7.56718i	−0.161822	−	0.603927i	−0.998424	−	0.0561165i	$-0.982128\pi$
$157$	−2.02762	−	7.56718i	−0.161822	−	0.603927i	0.836602	−	0.547810i	$-0.184538\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			3.52703i			0.277969i
$162$		0			0
$163$	4.89763	+	4.89763i	0.383612	+	0.383612i	0.872402	−	0.488789i	$-0.162561\pi$
$163$	4.89763	+	4.89763i	0.383612	+	0.383612i	−0.488789	+	0.872402i	$0.662561\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−18.7832	−	10.8445i	−1.45349	−	0.839174i	−0.454814	−	0.890587i	$-0.650294\pi$
$167$	−18.7832	−	10.8445i	−1.45349	−	0.839174i	−0.998677	+	0.0514129i	$0.983628\pi$
$168$		0			0
$169$	−9.66023	+	5.57734i	−0.743095	+	0.429026i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.05946	−	7.68601i	0.156578	−	0.584356i	−0.842387	−	0.538873i	$-0.818850\pi$
$173$	2.05946	−	7.68601i	0.156578	−	0.584356i	0.998965	−	0.0454836i	$-0.0144829\pi$
$174$		0			0
$175$	−5.06263	−	2.92291i	−0.382699	−	0.220951i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.47991	+	9.47991i	−0.708562	+	0.708562i	−0.966233	−	0.257671i	$-0.917045\pi$
$179$	−9.47991	+	9.47991i	−0.708562	+	0.708562i	0.257671	+	0.966233i	$0.417045\pi$
$180$		0			0
$181$	8.00075	+	8.00075i	0.594691	+	0.594691i	0.938895	−	0.344204i	$-0.111851\pi$
$181$	8.00075	+	8.00075i	0.594691	+	0.594691i	−0.344204	+	0.938895i	$0.611851\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.246822	−	0.427509i	0.0181467	−	0.0314311i
$186$		0			0
$187$	17.9324	+	4.80498i	1.31135	+	0.351375i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.22986	+	15.9866i	0.667850	+	1.15675i	0.978504	+	0.206227i	$0.0661184\pi$
$191$	9.22986	+	15.9866i	0.667850	+	1.15675i	−0.310655	+	0.950523i	$0.600548\pi$
$192$		0			0
$193$	2.61643	−	4.53179i	0.188335	−	0.326205i	−0.756360	−	0.654155i	$-0.773024\pi$
$193$	2.61643	−	4.53179i	0.188335	−	0.326205i	0.944695	+	0.327950i	$0.106358\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.3573	+	14.3573i	−1.02292	+	1.02292i	−0.0231869	+	0.999731i	$0.507381\pi$
$197$	−14.3573	+	14.3573i	−1.02292	+	1.02292i	−0.999731	+	0.0231869i	$0.992619\pi$
$198$		0			0
$199$	13.8358			0.980797			0.490399	−	0.871498i	$-0.336851\pi$
$199$	13.8358			0.980797			0.490399	+	0.871498i	$0.336851\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.81839	+	1.02314i	−0.267999	+	0.0718100i
$204$		0			0
$205$	−6.51038	−	1.74445i	−0.454705	−	0.121838i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.1632	−	5.86770i	0.703001	−	0.405878i
$210$		0			0
$211$	25.6481	−	6.87239i	1.76569	−	0.473115i	0.777831	−	0.628473i	$-0.216320\pi$
$211$	25.6481	−	6.87239i	1.76569	−	0.473115i	0.987858	+	0.155358i	$0.0496531\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	0.676538i		−	0.0461395i
$216$		0			0
$217$		−	7.87574i		−	0.534640i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−26.5146	+	7.10457i	−1.78357	+	0.477905i
$222$		0			0
$223$	−2.77266	+	1.60079i	−0.185671	+	0.107197i	−0.589954	−	0.807437i	$-0.700854\pi$
$223$	−2.77266	+	1.60079i	−0.185671	+	0.107197i	0.404284	+	0.914634i	$0.367521\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.78291	+	0.745680i	0.184708	+	0.0494925i	0.349988	−	0.936754i	$-0.386186\pi$
$227$	2.78291	+	0.745680i	0.184708	+	0.0494925i	−0.165279	+	0.986247i	$0.552852\pi$
$228$		0			0
$229$	−17.6277	+	4.72334i	−1.16487	+	0.312127i	−0.788911	−	0.614508i	$-0.789355\pi$
$229$	−17.6277	+	4.72334i	−1.16487	+	0.312127i	−0.375963	+	0.926635i	$0.622688\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.00585			−0.393456			−0.196728	−	0.980458i	$-0.563032\pi$
$233$	−6.00585			−0.393456			−0.196728	+	0.980458i	$0.563032\pi$
$234$		0			0
$235$	−5.97112	+	5.97112i	−0.389513	+	0.389513i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.00788	−	10.4059i	0.388617	−	0.673105i	−0.603647	−	0.797252i	$-0.706286\pi$
$239$	6.00788	−	10.4059i	0.388617	−	0.673105i	0.992264	+	0.124147i	$0.0396195\pi$
$240$		0			0
$241$	1.51923	+	2.63138i	0.0978622	+	0.169502i	0.910800	−	0.412849i	$-0.135466\pi$
$241$	1.51923	+	2.63138i	0.0978622	+	0.169502i	−0.812937	+	0.582351i	$0.802133\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.54317	−	0.949391i	−0.226365	−	0.0606543i
$246$		0			0
$247$	−8.67590	+	15.0271i	−0.552034	+	0.956152i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.95387	+	2.95387i	0.186447	+	0.186447i	0.794158	−	0.607711i	$-0.207912\pi$
$251$	2.95387	+	2.95387i	0.186447	+	0.186447i	−0.607711	+	0.794158i	$0.707912\pi$
$252$		0			0
$253$	−6.41937	+	6.41937i	−0.403582	+	0.403582i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.67398	−	0.966474i	−0.104420	−	0.0602870i	0.446880	−	0.894594i	$-0.352535\pi$
$257$	−1.67398	−	0.966474i	−0.104420	−	0.0602870i	−0.551301	+	0.834307i	$0.685868\pi$
$258$		0			0
$259$	0.239847	−	0.895122i	0.0149034	−	0.0556202i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.51993	+	0.877533i	−0.0937230	+	0.0541110i	−0.546129	−	0.837701i	$-0.683899\pi$
$263$	−1.51993	+	0.877533i	−0.0937230	+	0.0541110i	0.452406	+	0.891812i	$0.350566\pi$
$264$		0			0
$265$	0.507020	+	0.292728i	0.0311460	+	0.0179821i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.2013	+	14.2013i	0.865871	+	0.865871i	0.992012	−	0.126141i	$-0.0402592\pi$
$269$	14.2013	+	14.2013i	0.865871	+	0.865871i	−0.126141	+	0.992012i	$0.540259\pi$
$270$		0			0
$271$			11.3712i			0.690754i	0.938464	+	0.345377i	$0.112249\pi$
$271$			11.3712i			0.690754i	−0.938464	+	0.345377i	$0.887751\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.89439	−	14.5341i	−0.234841	−	0.876437i
$276$		0			0
$277$	1.81439	−	6.77138i	0.109016	−	0.406853i	−0.889754	−	0.456441i	$-0.849124\pi$
$277$	1.81439	−	6.77138i	0.109016	−	0.406853i	0.998770	+	0.0495877i	$0.0157907\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.16379	−	8.94395i	−0.308046	−	0.533552i	0.669889	−	0.742461i	$-0.266342\pi$
$281$	−5.16379	−	8.94395i	−0.308046	−	0.533552i	−0.977935	+	0.208910i	$0.933008\pi$
$282$		0			0
$283$	−6.25018	−	23.3260i	−0.371535	−	1.38659i	−0.858342	−	0.513078i	$-0.828505\pi$
$283$	−6.25018	−	23.3260i	−0.371535	−	1.38659i	0.486807	−	0.873509i	$-0.338161\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.6528			−0.746871
$288$		0			0
$289$	−14.1948			−0.834987
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.04554	+	18.8302i	0.294763	+	1.10007i	0.941405	+	0.337278i	$0.109506\pi$
$293$	5.04554	+	18.8302i	0.294763	+	1.10007i	−0.646642	+	0.762794i	$0.723827\pi$
$294$		0			0
$295$	−1.70109	−	2.94638i	−0.0990414	−	0.171545i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.47416	−	12.9658i	0.200916	−	0.749829i
$300$		0			0
$301$	−0.328709	−	1.22676i	−0.0189465	−	0.0707093i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	7.71230i		−	0.441605i
$306$		0			0
$307$	4.37646	+	4.37646i	0.249778	+	0.249778i	0.820879	−	0.571101i	$-0.193484\pi$
$307$	4.37646	+	4.37646i	0.249778	+	0.249778i	−0.571101	+	0.820879i	$0.693484\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.65273	−	1.53155i	−0.150423	−	0.0868465i	0.422900	−	0.906177i	$-0.361012\pi$
$311$	−2.65273	−	1.53155i	−0.150423	−	0.0868465i	−0.573322	+	0.819330i	$0.694346\pi$
$312$		0			0
$313$	−2.59526	+	1.49837i	−0.146693	+	0.0846930i	−0.571550	−	0.820567i	$-0.693658\pi$
$313$	−2.59526	+	1.49837i	−0.146693	+	0.0846930i	0.424857	+	0.905260i	$0.360324\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.47692	+	9.24401i	−0.139118	+	0.519195i	0.860829	+	0.508894i	$0.169946\pi$
$317$	−2.47692	+	9.24401i	−0.139118	+	0.519195i	−0.999947	+	0.0103009i	$0.996721\pi$
$318$		0			0
$319$	−8.81182	−	5.08751i	−0.493367	−	0.284846i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−13.9434	+	13.9434i	−0.775834	+	0.775834i
$324$		0			0
$325$	15.7317	+	15.7317i	0.872636	+	0.872636i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.92619	+	13.7286i	−0.436985	+	0.756880i
$330$		0			0
$331$	−14.5870	−	3.90856i	−0.801772	−	0.214834i	−0.165410	−	0.986225i	$-0.552895\pi$
$331$	−14.5870	−	3.90856i	−0.801772	−	0.214834i	−0.636362	+	0.771391i	$0.719561\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.0392949	+	0.0680608i	0.00214691	+	0.00371856i
$336$		0			0
$337$	1.09448	−	1.89569i	0.0596200	−	0.103265i	−0.834675	−	0.550743i	$-0.814344\pi$
$337$	1.09448	−	1.89569i	0.0596200	−	0.103265i	0.894295	+	0.447478i	$0.147678\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	14.3342	−	14.3342i	0.776242	−	0.776242i
$342$		0			0
$343$	−15.9258			−0.859912
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−27.6810	+	7.41711i	−1.48599	+	0.398171i	−0.908382	−	0.418140i	$-0.862682\pi$
$347$	−27.6810	+	7.41711i	−1.48599	+	0.398171i	−0.577612	+	0.816311i	$0.696015\pi$
$348$		0			0
$349$	−23.0850	−	6.18561i	−1.23571	−	0.331108i	−0.418911	−	0.908027i	$-0.637588\pi$
$349$	−23.0850	−	6.18561i	−1.23571	−	0.331108i	−0.816801	+	0.576919i	$0.804255\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.355770	−	0.205404i	0.0189357	−	0.0109325i	−0.490502	−	0.871440i	$-0.663187\pi$
$353$	0.355770	−	0.205404i	0.0189357	−	0.0109325i	0.509438	+	0.860507i	$0.329853\pi$
$354$		0			0
$355$	0.0297620	−	0.00797469i	0.00157960	−	0.000423253i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	1.19383i		−	0.0630078i	−0.999504	−	0.0315039i	$-0.989970\pi$
$359$		−	1.19383i		−	0.0630078i	0.999504	−	0.0315039i	$-0.0100297\pi$
$360$		0			0
$361$		−	6.53512i		−	0.343954i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−8.83291	+	2.36677i	−0.462336	+	0.123883i
$366$		0			0
$367$	−16.1698	+	9.33562i	−0.844055	+	0.487316i	−0.858641	−	0.512578i	$-0.828690\pi$
$367$	−16.1698	+	9.33562i	−0.844055	+	0.487316i	0.0145854	+	0.999894i	$0.495357\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.06160	+	0.284455i	0.0551156	+	0.0147682i
$372$		0			0
$373$	11.5442	−	3.09325i	0.597735	−	0.160163i	0.0527491	−	0.998608i	$-0.483202\pi$
$373$	11.5442	−	3.09325i	0.597735	−	0.160163i	0.544986	+	0.838445i	$0.316535\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.0446			0.774838
$378$		0			0
$379$	−15.3650	+	15.3650i	−0.789248	+	0.789248i	−0.981371	−	0.192123i	$-0.938463\pi$
$379$	−15.3650	+	15.3650i	−0.789248	+	0.789248i	0.192123	+	0.981371i	$0.438463\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.1162	+	19.2539i	−0.568013	+	0.983827i	0.428750	+	0.903423i	$0.358954\pi$
$383$	−11.1162	+	19.2539i	−0.568013	+	0.983827i	−0.996762	+	0.0804037i	$0.974379\pi$
$384$		0			0
$385$	1.47643	+	2.55725i	0.0752458	+	0.130330i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−15.6338	−	4.18905i	−0.792663	−	0.212393i	−0.160303	−	0.987068i	$-0.551247\pi$
$389$	−15.6338	−	4.18905i	−0.792663	−	0.212393i	−0.632360	+	0.774675i	$0.717914\pi$
$390$		0			0
$391$	7.62718	−	13.2107i	0.385723	−	0.668092i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.40449	−	1.40449i	−0.0706674	−	0.0706674i
$396$		0			0
$397$	14.5828	−	14.5828i	0.731887	−	0.731887i	−0.239106	−	0.970993i	$-0.576854\pi$
$397$	14.5828	−	14.5828i	0.731887	−	0.731887i	0.970993	+	0.239106i	$0.0768543\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−27.9585	−	16.1418i	−1.39618	−	0.806085i	−0.402191	−	0.915556i	$-0.631751\pi$
$401$	−27.9585	−	16.1418i	−1.39618	−	0.806085i	−0.993990	+	0.109470i	$0.965085\pi$
$402$		0			0
$403$	−7.75768	+	28.9521i	−0.386438	+	1.44220i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.06570	−	1.19263i	0.102393	−	0.0591166i
$408$		0			0
$409$	12.9975	+	7.50409i	0.642683	+	0.371053i	0.785647	−	0.618674i	$-0.212330\pi$
$409$	12.9975	+	7.50409i	0.642683	+	0.371053i	−0.142964	+	0.989728i	$0.545663\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.51613	−	4.51613i	−0.222224	−	0.222224i
$414$		0			0
$415$		−	2.70320i		−	0.132695i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.00718	+	22.4191i	0.293470	+	1.09525i	0.942425	+	0.334418i	$0.108540\pi$
$419$	6.00718	+	22.4191i	0.293470	+	1.09525i	−0.648955	+	0.760827i	$0.724794\pi$
$420$		0			0
$421$	4.05109	−	15.1189i	0.197438	−	0.736849i	−0.794184	−	0.607677i	$-0.792101\pi$
$421$	4.05109	−	15.1189i	0.197438	−	0.736849i	0.991622	−	0.129172i	$-0.0412319\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.6415	+	21.8958i	0.613205	+	1.06210i
$426$		0			0
$427$	−3.74717	−	13.9846i	−0.181338	−	0.676764i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.63818			−0.0789082			−0.0394541	−	0.999221i	$-0.512562\pi$
$431$	−1.63818			−0.0789082			−0.0394541	+	0.999221i	$0.512562\pi$
$432$		0			0
$433$	24.1284			1.15954			0.579769	−	0.814781i	$-0.303143\pi$
$433$	24.1284			1.15954			0.579769	+	0.814781i	$0.303143\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.49571	−	9.31411i	−0.119386	−	0.445554i
$438$		0			0
$439$	−6.04546	−	10.4711i	−0.288534	−	0.499756i	0.684926	−	0.728613i	$-0.259835\pi$
$439$	−6.04546	−	10.4711i	−0.288534	−	0.499756i	−0.973460	+	0.228857i	$0.926501\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.35450	+	16.2512i	−0.206889	+	0.772119i	0.781977	+	0.623307i	$0.214211\pi$
$443$	−4.35450	+	16.2512i	−0.206889	+	0.772119i	−0.988866	+	0.148811i	$0.952455\pi$
$444$		0			0
$445$	−2.26761	−	8.46284i	−0.107495	−	0.401177i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			31.8270i			1.50201i	0.660298	+	0.751004i	$0.270430\pi$
$449$			31.8270i			1.50201i	−0.660298	+	0.751004i	$0.729570\pi$
$450$		0			0
$451$	−23.0287	−	23.0287i	−1.08438	−	1.08438i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.78111	−	2.18303i	−0.177261	−	0.102342i
$456$		0			0
$457$	−24.8553	+	14.3502i	−1.16268	+	0.671275i	−0.951945	−	0.306268i	$-0.900920\pi$
$457$	−24.8553	+	14.3502i	−1.16268	+	0.671275i	−0.210737	+	0.977543i	$0.567586\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.483918	+	1.80601i	−0.0225383	+	0.0841141i	−0.976279	−	0.216517i	$-0.930530\pi$
$461$	−0.483918	+	1.80601i	−0.0225383	+	0.0841141i	0.953741	+	0.300631i	$0.0971971\pi$
$462$		0			0
$463$	4.71990	+	2.72503i	0.219352	+	0.126643i	0.605650	−	0.795731i	$-0.292913\pi$
$463$	4.71990	+	2.72503i	0.219352	+	0.126643i	−0.386298	+	0.922374i	$0.626246\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.95228	−	8.95228i	0.414262	−	0.414262i	−0.468958	−	0.883220i	$-0.655370\pi$
$467$	8.95228	−	8.95228i	0.414262	−	0.414262i	0.883220	+	0.468958i	$0.155370\pi$
$468$		0			0
$469$	0.104322	+	0.104322i	0.00481713	+	0.00481713i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.63450	−	2.83103i	0.0751542	−	0.130171i
$474$		0			0
$475$	15.4375	+	4.13647i	0.708321	+	0.189794i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.27809	−	7.40987i	−0.195471	−	0.338566i	0.751584	−	0.659638i	$-0.229290\pi$
$479$	−4.27809	−	7.40987i	−0.195471	−	0.338566i	−0.947055	+	0.321072i	$0.895957\pi$
$480$		0			0
$481$	−1.76341	+	3.05431i	−0.0804045	+	0.139265i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.29093	−	4.29093i	0.194841	−	0.194841i
$486$		0			0
$487$	13.1689			0.596738			0.298369	−	0.954451i	$-0.403557\pi$
$487$	13.1689			0.596738			0.298369	+	0.954451i	$0.403557\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.09692	−	2.16956i	0.365409	−	0.0979110i	−0.0714425	−	0.997445i	$-0.522760\pi$
$491$	8.09692	−	2.16956i	0.365409	−	0.0979110i	0.436851	+	0.899534i	$0.356094\pi$
$492$		0			0
$493$	16.5145	+	4.42505i	0.743776	+	0.199294i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.0500924	−	0.0289209i	0.00224695	−	0.00129728i
$498$		0			0
$499$	−31.2957	+	8.38567i	−1.40099	+	0.375394i	−0.878700	−	0.477374i	$-0.841589\pi$
$499$	−31.2957	+	8.38567i	−1.40099	+	0.375394i	−0.522289	+	0.852768i	$0.674922\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			20.8126i			0.927989i	0.885838	+	0.463994i	$0.153584\pi$
$503$			20.8126i			0.927989i	−0.885838	+	0.463994i	$0.846416\pi$
$504$		0			0
$505$		−	5.00321i		−	0.222640i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	20.7078	−	5.54865i	0.917859	−	0.245940i	0.231189	−	0.972909i	$-0.425738\pi$
$509$	20.7078	−	5.54865i	0.917859	−	0.245940i	0.686670	+	0.726969i	$0.259072\pi$
$510$		0			0
$511$	−14.8667	+	8.58329i	−0.657664	+	0.379703i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.6342	+	3.38533i	0.556730	+	0.149175i
$516$		0			0
$517$	−39.4127	+	10.5606i	−1.73337	+	0.464455i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−20.1534			−0.882938			−0.441469	−	0.897277i	$-0.645542\pi$
$521$	−20.1534			−0.882938			−0.441469	+	0.897277i	$0.645542\pi$
$522$		0			0
$523$	−14.7713	+	14.7713i	−0.645905	+	0.645905i	−0.952001	−	0.306096i	$-0.900977\pi$
$523$	−14.7713	+	14.7713i	−0.645905	+	0.645905i	0.306096	+	0.952001i	$0.400977\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−17.0312	+	29.4990i	−0.741892	+	1.28499i
$528$		0			0
$529$	−7.77028	−	13.4585i	−0.337838	−	0.585153i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	46.5131	+	12.4631i	2.01470	+	0.539838i
$534$		0			0
$535$	4.03149	−	6.98274i	0.174296	−	0.301890i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−12.5330	−	12.5330i	−0.539835	−	0.539835i
$540$		0			0
$541$	11.1739	−	11.1739i	0.480403	−	0.480403i	−0.424857	−	0.905260i	$-0.639676\pi$
$541$	11.1739	−	11.1739i	0.480403	−	0.480403i	0.905260	+	0.424857i	$0.139676\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	12.1153	+	6.99478i	0.518963	+	0.299624i
$546$		0			0
$547$	3.23236	−	12.0633i	0.138206	−	0.515791i	−0.861758	−	0.507319i	$-0.830637\pi$
$547$	3.23236	−	12.0633i	0.138206	−	0.515791i	0.999964	−	0.00847177i	$-0.00269668\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.35956	−	5.40375i	0.398731	−	0.230207i
$552$		0			0
$553$	−3.22914	−	1.86435i	−0.137317	−	0.0792800i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.41323	+	4.41323i	0.186995	+	0.186995i	0.794395	−	0.607401i	$-0.207788\pi$
$557$	4.41323	+	4.41323i	0.186995	+	0.186995i	−0.607401	+	0.794395i	$0.707788\pi$
$558$		0			0
$559$			4.83349i			0.204435i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.09152	−	33.9300i	−0.383162	−	1.42998i	−0.841044	−	0.540967i	$-0.818058\pi$
$563$	−9.09152	−	33.9300i	−0.383162	−	1.42998i	0.457882	−	0.889013i	$-0.348608\pi$
$564$		0			0
$565$	0.449782	−	1.67861i	0.0189225	−	0.0706197i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	10.8432	+	18.7810i	0.454572	+	0.787342i	0.998663	−	0.0516841i	$-0.0164589\pi$
$569$	10.8432	+	18.7810i	0.454572	+	0.787342i	−0.544091	+	0.839026i	$0.683126\pi$
$570$		0			0
$571$	−2.69081	−	10.0422i	−0.112607	−	0.420255i	0.886490	−	0.462748i	$-0.153137\pi$
$571$	−2.69081	−	10.0422i	−0.112607	−	0.420255i	−0.999097	+	0.0424934i	$0.986470\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.3635			−0.515595
$576$		0			0
$577$	−33.2014			−1.38219			−0.691096	−	0.722763i	$-0.742872\pi$
$577$	−33.2014			−1.38219			−0.691096	+	0.722763i	$0.742872\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.31340	−	4.90169i	−0.0544891	−	0.203356i
$582$		0			0
$583$	1.41444	+	2.44989i	0.0585803	+	0.101464i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.554497	+	2.06941i	−0.0228865	+	0.0854137i	−0.976425	−	0.215859i	$-0.930745\pi$
$587$	−0.554497	+	2.06941i	−0.0228865	+	0.0854137i	0.953538	+	0.301273i	$0.0974115\pi$
$588$		0			0
$589$	5.57282	+	20.7981i	0.229624	+	0.856969i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	13.9278i		−	0.571945i	−0.958238	−	0.285973i	$-0.907683\pi$
$593$		−	13.9278i		−	0.571945i	0.958238	−	0.285973i	$-0.0923166\pi$
$594$		0			0
$595$	−3.50844	−	3.50844i	−0.143832	−	0.143832i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	20.2130	+	11.6700i	0.825881	+	0.476823i	0.852440	−	0.522825i	$-0.175122\pi$
$599$	20.2130	+	11.6700i	0.825881	+	0.476823i	−0.0265594	+	0.999647i	$0.508455\pi$
$600$		0			0
$601$	−10.3379	+	5.96857i	−0.421691	+	0.243463i	−0.695800	−	0.718235i	$-0.744950\pi$
$601$	−10.3379	+	5.96857i	−0.421691	+	0.243463i	0.274110	+	0.961698i	$0.411617\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.00865733	+	0.0323096i	−0.000351971	+	0.00131357i
$606$		0			0
$607$	10.3919	+	5.99979i	0.421796	+	0.243524i	0.695845	−	0.718192i	$-0.255030\pi$
$607$	10.3919	+	5.99979i	0.421796	+	0.243524i	−0.274050	+	0.961716i	$0.588363\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	42.6603	−	42.6603i	1.72585	−	1.72585i
$612$		0			0
$613$	−18.1803	−	18.1803i	−0.734296	−	0.734296i	0.237172	−	0.971468i	$-0.423780\pi$
$613$	−18.1803	−	18.1803i	−0.734296	−	0.734296i	−0.971468	+	0.237172i	$0.923780\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.9672	+	32.8521i	−0.763589	+	1.32257i	0.177401	+	0.984139i	$0.443231\pi$
$617$	−18.9672	+	32.8521i	−0.763589	+	1.32257i	−0.940989	+	0.338436i	$0.890102\pi$
$618$		0			0
$619$	0.00230201		0.000616823i	9.25258e−5		2.47922e-5i	0.258865	−	0.965913i	$-0.416651\pi$
$619$	0.00230201		0.000616823i	9.25258e−5		2.47922e-5i	−0.258773	+	0.965938i	$0.583318\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.22368	−	14.2438i	−0.329475	−	0.570667i
$624$		0			0
$625$	9.06281	−	15.6972i	0.362512	−	0.627890i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.83406	+	2.83406i	−0.113001	+	0.113001i
$630$		0			0
$631$	39.2643			1.56309			0.781543	−	0.623852i	$-0.214433\pi$
$631$	39.2643			1.56309			0.781543	+	0.623852i	$0.214433\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−11.6387	+	3.11858i	−0.461868	+	0.123757i
$636$		0			0
$637$	25.3140	+	6.78286i	1.00298	+	0.268747i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15.2983	+	8.83246i	−0.604245	+	0.348861i	−0.770710	−	0.637186i	$-0.780098\pi$
$641$	−15.2983	+	8.83246i	−0.604245	+	0.348861i	0.166465	+	0.986047i	$0.446765\pi$
$642$		0			0
$643$	6.60298	−	1.76926i	0.260396	−	0.0697729i	−0.126259	−	0.991997i	$-0.540297\pi$
$643$	6.60298	−	1.76926i	0.260396	−	0.0697729i	0.386655	+	0.922224i	$0.373630\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			4.24252i			0.166791i	0.996517	+	0.0833953i	$0.0265764\pi$
$647$			4.24252i			0.166791i	−0.996517	+	0.0833953i	$0.973424\pi$
$648$		0			0
$649$		−	16.4392i		−	0.645293i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	26.6484	−	7.14041i	1.04283	−	0.279426i	0.303545	−	0.952817i	$-0.401830\pi$
$653$	26.6484	−	7.14041i	1.04283	−	0.279426i	0.739286	+	0.673391i	$0.235163\pi$
$654$		0			0
$655$	7.39431	−	4.26911i	0.288919	−	0.166808i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.1504	−	2.71978i	−0.395402	−	0.105948i	0.0556391	−	0.998451i	$-0.482280\pi$
$659$	−10.1504	−	2.71978i	−0.395402	−	0.105948i	−0.451041	+	0.892503i	$0.648947\pi$
$660$		0			0
$661$	−28.3410	+	7.59396i	−1.10234	+	0.295371i	−0.763717	−	0.645552i	$-0.776628\pi$
$661$	−28.3410	+	7.59396i	−1.10234	+	0.295371i	−0.338622	+	0.940922i	$0.609961\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.13641			−0.121625
$666$		0			0
$667$	−5.91179	+	5.91179i	−0.228905	+	0.228905i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	18.6327	−	32.2728i	0.719307	−	1.24588i
$672$		0			0
$673$	−5.32418	−	9.22175i	−0.205232	−	0.355472i	0.744975	−	0.667093i	$-0.232462\pi$
$673$	−5.32418	−	9.22175i	−0.205232	−	0.355472i	−0.950207	+	0.311621i	$0.899128\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.2938	−	5.70565i	−0.818387	−	0.219286i	−0.174746	−	0.984614i	$-0.555910\pi$
$677$	−21.2938	−	5.70565i	−0.818387	−	0.219286i	−0.643641	+	0.765327i	$0.722577\pi$
$678$		0			0
$679$	5.69587	−	9.86554i	0.218587	−	0.378605i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.68202	+	1.68202i	0.0643609	+	0.0643609i	0.738555	−	0.674194i	$-0.235509\pi$
$683$	1.68202	+	1.68202i	0.0643609	+	0.0643609i	−0.674194	+	0.738555i	$0.735509\pi$
$684$		0			0
$685$	−4.86488	+	4.86488i	−0.185877	+	0.185877i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.62237	−	2.09138i	−0.138001	−	0.0796751i
$690$		0			0
$691$	0.595784	−	2.22350i	0.0226647	−	0.0845858i	−0.953667	−	0.300864i	$-0.902725\pi$
$691$	0.595784	−	2.22350i	0.0226647	−	0.0845858i	0.976332	+	0.216278i	$0.0693917\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.848565	−	0.489919i	0.0321879	−	0.0185837i
$696$		0			0
$697$	47.3917	+	27.3616i	1.79509	+	1.03639i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−10.2728	−	10.2728i	−0.387997	−	0.387997i	0.485976	−	0.873972i	$-0.338464\pi$
$701$	−10.2728	−	10.2728i	−0.387997	−	0.387997i	−0.873972	+	0.485976i	$0.838464\pi$
$702$		0			0
$703$			2.53353i			0.0955540i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.43091	−	9.07228i	−0.0914238	−	0.341198i
$708$		0			0
$709$	1.30925	−	4.88619i	0.0491700	−	0.183505i	−0.936973	−	0.349401i	$-0.886385\pi$
$709$	1.30925	−	4.88619i	0.0491700	−	0.183505i	0.986143	+	0.165896i	$0.0530517\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−8.32834	−	14.4251i	−0.311899	−	0.540224i
$714$		0			0
$715$	−2.90859	−	10.8550i	−0.108775	−	0.405955i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.73858			0.251307			0.125653	−	0.992074i	$-0.459897\pi$
$719$	6.73858			0.251307			0.125653	+	0.992074i	$0.459897\pi$
$720$		0			0
$721$	24.5544			0.914452
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.58646	−	13.3849i	−0.133198	−	0.497101i
$726$		0			0
$727$	4.14056	+	7.17166i	0.153565	+	0.265982i	0.932536	−	0.361078i	$-0.117591\pi$
$727$	4.14056	+	7.17166i	0.153565	+	0.265982i	−0.778971	+	0.627060i	$0.784258\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.42166	+	5.30572i	−0.0525821	+	0.196239i
$732$		0			0
$733$	−11.7070	−	43.6909i	−0.432406	−	1.61376i	−0.747198	−	0.664601i	$-0.768601\pi$
$733$	−11.7070	−	43.6909i	−0.432406	−	1.61376i	0.314792	−	0.949161i	$-0.398065\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			0.379742i			0.0139880i
$738$		0			0
$739$	−22.0530	−	22.0530i	−0.811234	−	0.811234i	0.173585	−	0.984819i	$-0.444465\pi$
$739$	−22.0530	−	22.0530i	−0.811234	−	0.811234i	−0.984819	+	0.173585i	$0.944465\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	29.9386	+	17.2851i	1.09834	+	0.634128i	0.935785	−	0.352571i	$-0.114693\pi$
$743$	29.9386	+	17.2851i	1.09834	+	0.634128i	0.162557	+	0.986699i	$0.448026\pi$
$744$		0			0
$745$	−3.41062	+	1.96912i	−0.124955	+	0.0721431i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.91756	−	14.6205i	0.143144	−	0.534222i
$750$		0			0
$751$	38.8676	+	22.4402i	1.41830	+	0.818855i	0.996149	−	0.0876713i	$-0.0279425\pi$
$751$	38.8676	+	22.4402i	1.41830	+	0.818855i	0.422149	+	0.906526i	$0.361276\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−7.88134	+	7.88134i	−0.286832	+	0.286832i
$756$		0			0
$757$	27.6111	+	27.6111i	1.00354	+	1.00354i	0.999994	+	0.00354931i	$0.00112978\pi$
$757$	27.6111	+	27.6111i	1.00354	+	1.00354i	0.00354931	+	0.999994i	$0.498870\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	17.8578	−	30.9307i	0.647346	−	1.12124i	−0.336408	−	0.941716i	$-0.609212\pi$
$761$	17.8578	−	30.9307i	0.647346	−	1.12124i	0.983754	−	0.179520i	$-0.0574545\pi$
$762$		0			0
$763$	25.3672	+	6.79711i	0.918353	+	0.246072i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.1534	+	21.0502i	0.438832	+	0.760079i
$768$		0			0
$769$	−22.6077	+	39.1577i	−0.815254	+	1.41206i	0.0938910	+	0.995582i	$0.470069\pi$
$769$	−22.6077	+	39.1577i	−0.815254	+	1.41206i	−0.909145	+	0.416479i	$0.863264\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−5.57961	+	5.57961i	−0.200685	+	0.200685i	−0.800293	−	0.599609i	$-0.795323\pi$
$773$	−5.57961	+	5.57961i	−0.200685	+	0.200685i	0.599609	+	0.800293i	$0.295323\pi$
$774$		0			0
$775$	27.6073			0.991684
$776$		0			0
$777$		0			0
$778$		0			0
$779$	33.4132	−	8.95305i	1.19715	−	0.320776i
$780$		0			0
$781$	0.143808	+	0.0385333i	0.00514586	+	0.00137883i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.66717	+	2.69459i	−0.166578	+	0.0961741i
$786$		0			0
$787$	−8.95529	+	2.39956i	−0.319221	+	0.0855351i	−0.414872	−	0.909880i	$-0.636174\pi$
$787$	−8.95529	+	2.39956i	−0.319221	+	0.0855351i	0.0956504	+	0.995415i	$0.469507\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	3.26235i		−	0.115996i
$792$		0			0
$793$			55.1001i			1.95666i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	24.5310	−	6.57307i	0.868934	−	0.232830i	0.203307	−	0.979115i	$-0.434831\pi$
$797$	24.5310	−	6.57307i	0.868934	−	0.232830i	0.665627	+	0.746285i	$0.268164\pi$
$798$		0			0
$799$	59.3759	−	34.2807i	2.10057	−	1.21276i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−42.6801	−	11.4361i	−1.50615	−	0.403571i
$804$		0			0
$805$	2.34361	−	0.627969i	0.0826014	−	0.0221330i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−33.1931			−1.16701			−0.583503	−	0.812111i	$-0.698318\pi$
$809$	−33.1931			−1.16701			−0.583503	+	0.812111i	$0.698318\pi$
$810$		0			0
$811$	−7.35128	+	7.35128i	−0.258138	+	0.258138i	−0.824297	−	0.566158i	$-0.808429\pi$
$811$	−7.35128	+	7.35128i	−0.258138	+	0.258138i	0.566158	+	0.824297i	$0.308429\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.38234	−	4.12633i	0.0834497	−	0.144539i
$816$		0			0
$817$	1.73610	+	3.00701i	0.0607383	+	0.105202i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−38.6179	−	10.3476i	−1.34777	−	0.361135i	−0.488462	−	0.872585i	$-0.662442\pi$
$821$	−38.6179	−	10.3476i	−1.34777	−	0.361135i	−0.859313	+	0.511450i	$0.829109\pi$
$822$		0			0
$823$	−11.8717	+	20.5623i	−0.413821	+	0.716758i	−0.995304	−	0.0968000i	$-0.969139\pi$
$823$	−11.8717	+	20.5623i	−0.413821	+	0.716758i	0.581483	+	0.813558i	$0.302473\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	25.1545	+	25.1545i	0.874708	+	0.874708i	0.992981	−	0.118273i	$-0.0377357\pi$
$827$	25.1545	+	25.1545i	0.874708	+	0.874708i	−0.118273	+	0.992981i	$0.537736\pi$
$828$		0			0
$829$	6.12372	−	6.12372i	0.212686	−	0.212686i	−0.592722	−	0.805407i	$-0.701947\pi$
$829$	6.12372	−	6.12372i	0.212686	−	0.212686i	0.805407	+	0.592722i	$0.201947\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	25.7922	+	14.8911i	0.893646	+	0.515947i
$834$		0			0
$835$	−3.86161	+	14.4117i	−0.133637	+	0.498739i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−35.2084	+	20.3276i	−1.21553	+	0.701786i	−0.963958	−	0.266054i	$-0.914280\pi$
$839$	−35.2084	+	20.3276i	−1.21553	+	0.701786i	−0.251570	+	0.967839i	$0.580947\pi$
$840$		0			0
$841$	16.9997	+	9.81476i	0.586195	+	0.338440i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.42593	+	5.42593i	0.186658	+	0.186658i
$846$		0			0
$847$			0.0627931i			0.00215760i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.507262	−	1.89313i	−0.0173887	−	0.0648955i
$852$		0			0
$853$	11.1499	−	41.6120i	0.381765	−	1.42477i	−0.461437	−	0.887173i	$-0.652666\pi$
$853$	11.1499	−	41.6120i	0.381765	−	1.42477i	0.843203	−	0.537595i	$-0.180667\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.72246	−	8.17953i	−0.161316	−	0.279408i	0.774025	−	0.633155i	$-0.218241\pi$
$857$	−4.72246	−	8.17953i	−0.161316	−	0.279408i	−0.935341	+	0.353748i	$0.884907\pi$
$858$		0			0
$859$	5.87045	+	21.9088i	0.200297	+	0.747519i	0.990832	+	0.135102i	$0.0431361\pi$
$859$	5.87045	+	21.9088i	0.200297	+	0.747519i	−0.790535	+	0.612417i	$0.790197\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.58147			−0.121915			−0.0609573	−	0.998140i	$-0.519415\pi$
$863$	−3.58147			−0.121915			−0.0609573	+	0.998140i	$0.519415\pi$
$864$		0			0
$865$	−5.47380			−0.186115
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.48399	−	9.27039i	−0.0842637	−	0.314476i
$870$		0			0
$871$	−0.280740	−	0.486256i	−0.00951252	−	0.0164762i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.19044	+	8.17482i	−0.0740503	+	0.276359i
$876$		0			0
$877$	4.52743	+	16.8966i	0.152881	+	0.570558i	0.999278	+	0.0380056i	$0.0121005\pi$
$877$	4.52743	+	16.8966i	0.152881	+	0.570558i	−0.846397	+	0.532553i	$0.821233\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	46.1363i		−	1.55437i	−0.629272	−	0.777185i	$-0.716647\pi$
$881$		−	46.1363i		−	1.55437i	0.629272	−	0.777185i	$-0.283353\pi$
$882$		0			0
$883$	−19.7311	−	19.7311i	−0.664003	−	0.664003i	0.292318	−	0.956321i	$-0.405573\pi$
$883$	−19.7311	−	19.7311i	−0.664003	−	0.664003i	−0.956321	+	0.292318i	$0.905573\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.7760	+	17.1912i	0.999780	+	0.577223i	0.908183	−	0.418573i	$-0.137470\pi$
$887$	29.7760	+	17.1912i	0.999780	+	0.577223i	0.0915965	+	0.995796i	$0.470803\pi$
$888$		0			0
$889$	−19.5891	+	11.3098i	−0.656999	+	0.379318i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	11.2171	−	41.8626i	0.375364	−	1.40088i
$894$		0			0
$895$	7.98697	+	4.61128i	0.266975	+	0.154138i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	13.2008	−	13.2008i	0.440272	−	0.440272i
$900$		0			0
$901$	−3.36115	−	3.36115i	−0.111976	−	0.111976i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.89178	−	6.74076i	0.129367	−	0.224070i
$906$		0			0
$907$	53.7121	+	14.3921i	1.78348	+	0.477883i	0.991211	−	0.132287i	$-0.0422322\pi$
$907$	53.7121	+	14.3921i	1.78348	+	0.477883i	0.792271	+	0.610170i	$0.208899\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.01435	−	10.4172i	−0.199264	−	0.345136i	0.749026	−	0.662541i	$-0.230522\pi$
$911$	−6.01435	−	10.4172i	−0.199264	−	0.345136i	−0.948290	+	0.317405i	$0.897189\pi$
$912$		0			0
$913$	6.53085	−	11.3118i	0.216140	−	0.374365i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	11.3338	−	11.3338i	0.374275	−	0.374275i
$918$		0			0
$919$	11.8860			0.392084			0.196042	−	0.980595i	$-0.437191\pi$
$919$	11.8860			0.392084			0.196042	+	0.980595i	$0.437191\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.212633	+	0.0569747i	−0.00699889	+	0.00187535i
$924$		0			0
$925$	3.13773	+	0.840752i	0.103168	+	0.0276438i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.44934	−	1.99148i	0.113169	−	0.0653382i	−0.442347	−	0.896844i	$-0.645854\pi$
$929$	3.44934	−	1.99148i	0.113169	−	0.0653382i	0.555516	+	0.831506i	$0.312521\pi$
$930$		0			0
$931$	18.1846	−	4.87255i	0.595977	−	0.159692i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	12.7711i		−	0.417659i
$936$		0			0
$937$		−	26.0017i		−	0.849438i	−0.905325	−	0.424719i	$-0.860373\pi$
$937$		−	26.0017i		−	0.849438i	0.905325	−	0.424719i	$-0.139627\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	41.3717	−	11.0855i	1.34868	−	0.361378i	0.489033	−	0.872265i	$-0.337350\pi$
$941$	41.3717	−	11.0855i	1.34868	−	0.361378i	0.859648	+	0.510888i	$0.170683\pi$
$942$		0			0
$943$	−23.1747	+	13.3799i	−0.754673	+	0.435710i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	17.6066	+	4.71769i	0.572139	+	0.153304i	0.533277	−	0.845940i	$-0.320960\pi$
$947$	17.6066	+	4.71769i	0.572139	+	0.153304i	0.0388617	+	0.999245i	$0.487627\pi$
$948$		0			0
$949$	63.1062	−	16.9093i	2.04851	−	0.548898i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−16.9031			−0.547545			−0.273772	−	0.961795i	$-0.588271\pi$
$953$	−16.9031			−0.547545			−0.273772	+	0.961795i	$0.588271\pi$
$954$		0			0
$955$	8.97930	−	8.97930i	0.290563	−	0.290563i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−6.45774	+	11.1851i	−0.208531	+	0.361187i
$960$		0			0
$961$	3.09688	+	5.36395i	0.0998993	+	0.173031i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.47708	−	0.931682i	−0.111931	−	0.0299919i
$966$		0			0
$967$	−1.50617	+	2.60876i	−0.0484351	+	0.0838921i	−0.889227	−	0.457467i	$-0.848757\pi$
$967$	−1.50617	+	2.60876i	−0.0484351	+	0.0838921i	0.840791	+	0.541359i	$0.182090\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−35.4934	−	35.4934i	−1.13904	−	1.13904i	−0.988623	−	0.150413i	$-0.951940\pi$
$971$	−35.4934	−	35.4934i	−1.13904	−	1.13904i	−0.150413	−	0.988623i	$-0.548060\pi$
$972$		0			0
$973$	1.30066	−	1.30066i	0.0416972	−	0.0416972i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.03784	−	4.64065i	−0.257153	−	0.148467i	0.365882	−	0.930661i	$-0.380767\pi$
$977$	−8.03784	−	4.64065i	−0.257153	−	0.148467i	−0.623035	+	0.782194i	$0.714101\pi$
$978$		0			0
$979$	10.9570	−	40.8920i	0.350186	−	1.30691i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	11.0480	−	6.37856i	0.352376	−	0.203444i	−0.313355	−	0.949636i	$-0.601453\pi$
$983$	11.0480	−	6.37856i	0.352376	−	0.203444i	0.665731	+	0.746192i	$0.268120\pi$
$984$		0			0
$985$	12.0963	+	6.98379i	0.385420	+	0.222522i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.89932	−	1.89932i	−0.0603949	−	0.0603949i
$990$		0			0
$991$		−	6.60967i		−	0.209963i	−0.994474	−	0.104982i	$-0.966522\pi$
$991$		−	6.60967i		−	0.209963i	0.994474	−	0.104982i	$-0.0334784\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.46340	−	9.19352i	−0.0780949	−	0.291454i
$996$		0			0
$997$	−9.80194	+	36.5814i	−0.310431	+	1.15854i	0.617738	+	0.786384i	$0.288049\pi$
$997$	−9.80194	+	36.5814i	−0.310431	+	1.15854i	−0.928169	+	0.372159i	$0.878618\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.z.a.719.10		88
3.2	odd	2		576.2.y.a.527.5		88
4.3	odd	2		432.2.v.a.395.15		88
9.2	odd	6	inner	1728.2.z.a.143.10		88
9.7	even	3		576.2.y.a.335.7		88
12.11	even	2		144.2.u.a.59.8	yes	88
16.3	odd	4	inner	1728.2.z.a.1583.10		88
16.13	even	4		432.2.v.a.179.8		88
36.7	odd	6		144.2.u.a.11.15	✓	88
36.11	even	6		432.2.v.a.251.8		88
48.29	odd	4		144.2.u.a.131.15	yes	88
48.35	even	4		576.2.y.a.239.7		88
144.29	odd	12		432.2.v.a.35.15		88
144.61	even	12		144.2.u.a.83.8	yes	88
144.83	even	12	inner	1728.2.z.a.1007.10		88
144.115	odd	12		576.2.y.a.47.5		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.15	✓	88	36.7	odd	6
144.2.u.a.59.8	yes	88	12.11	even	2
144.2.u.a.83.8	yes	88	144.61	even	12
144.2.u.a.131.15	yes	88	48.29	odd	4
432.2.v.a.35.15		88	144.29	odd	12
432.2.v.a.179.8		88	16.13	even	4
432.2.v.a.251.8		88	36.11	even	6
432.2.v.a.395.15		88	4.3	odd	2
576.2.y.a.47.5		88	144.115	odd	12
576.2.y.a.239.7		88	48.35	even	4
576.2.y.a.335.7		88	9.7	even	3
576.2.y.a.527.5		88	3.2	odd	2
1728.2.z.a.143.10		88	9.2	odd	6	inner
1728.2.z.a.719.10		88	1.1	even	1	trivial
1728.2.z.a.1007.10		88	144.83	even	12	inner
1728.2.z.a.1583.10		88	16.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.178044 - 0.664471i) q^{5} +(-0.645693 - 1.11837i) q^{7} +(0.860301 - 3.21069i) q^{11} +(1.27203 + 4.74727i) q^{13} +5.58523i q^{17} +(2.49649 + 2.49649i) q^{19} +(-2.36529 - 1.36560i) q^{23} +(3.92031 - 2.26339i) q^{25} +(0.792277 - 2.95682i) q^{29} +(5.28160 + 3.04933i) q^{31} +(-0.628165 + 0.628165i) q^{35} +(0.507420 + 0.507420i) q^{37} +(4.89892 - 8.48518i) q^{41} +(0.949956 + 0.254540i) q^{43} +(-6.13774 - 10.6309i) q^{47} +(2.66616 - 4.61793i) q^{49} +(-0.601793 + 0.601793i) q^{53} -2.28658 q^{55} +(4.77715 - 1.28003i) q^{59} +(10.8292 + 2.90167i) q^{61} +(2.92795 - 1.69045i) q^{65} +(-0.110351 + 0.0295686i) q^{67} +0.0447904i q^{71} -13.2931i q^{73} +(-4.14624 + 1.11098i) q^{77} +(2.50052 - 1.44368i) q^{79} +(3.79568 + 1.01705i) q^{83} +(3.71122 - 0.994419i) q^{85} +12.7362 q^{89} +(4.48788 - 4.48788i) q^{91} +(1.21436 - 2.10333i) q^{95} +(4.41066 + 7.63949i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Introduction

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Modular forms

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Database

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